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Hysteresis and Hopf bifurcation: Deciphering the dynamics of an in-host model of SARS-CoV-2 with logistic target cell growth and sigmoidal immune response

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  • Kumawat, Nitesh
  • Rashid, Mubasher
  • Srivastava, Akriti
  • Tripathi, Jai Prakash

Abstract

Mathematical models of in-host dynamics of SARS-CoV-2 may reveal the intricate underlying dynamics of host-pathogen interaction and guide crucial steps to curtail progression of COVID-19 and other similar infectious diseases. While the existing models on SARS-CoV-2 have considered a wide range of host-pathogen interactions, at their core, these models are remarkably similar, particularly in the choice of mathematical functions used in modeling the interactions. Specifically, these models have employed mass action kinetics while modeling target-cell interaction with virus particles and immune response to virus, thus overlooking the role of saturated evolution of target epithelial cells as well as immune cells. Here we fill this gap by developing a more comprehensive model of in-host dynamics of SARS-CoV-2 that concurrently models target epithelial cell growth using a logistic equation and virus-immune interaction using Michaelis–Menten kinetics. We identify a feasible disease-free equilibrium whose local stability depends on ”reproduction number” and global stability on the replenishment rate as well as the removal rate of immune cells. We also obtain multiple endemic equilibria and perform their local and global stability analysis. Our detailed numerical investigation demonstrates that the infection rate and reproduction number govern several interesting dynamical behaviors such as forward bifurcation with and without hysteresis, Hopf bifurcation, and multiple endemic equilibria. To analyze the impact of parameters on the model system and disease dynamics, we investigate several sensitive parameters and compute their sensitivity indices. Finally, to understand the impact of anti-viral therapy on viral load, we identify a novel threshold of replication rate that must be crossed to enable virus proliferation. Our results thus provide novel insights into the in-host dynamics of SARS-CoV-2 and we expect this model will help in the development of better treatment strategies for COVID-19 and other such infectious diseases.

Suggested Citation

  • Kumawat, Nitesh & Rashid, Mubasher & Srivastava, Akriti & Tripathi, Jai Prakash, 2023. "Hysteresis and Hopf bifurcation: Deciphering the dynamics of an in-host model of SARS-CoV-2 with logistic target cell growth and sigmoidal immune response," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010536
    DOI: 10.1016/j.chaos.2023.114151
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